# Combinatorial problems in genomics and computational biology

Presented by Richard Karp on 201001261232

Discovery of protein modules

- networks: fundamental units of natural selection
- protein complexes, signalling pathways
- conservation across species
- Sharan et al (PNAS 2005)
- topology free alignment, Bruckner et al (RECOMB 2009)
- NP-hard, exact solutions are slow, not practical
- idea: use heuristics

Multiple genome alignment

- find a multiple alignment that maximizes sum of weights of aligned anchor pairs
- 2 genomes is the maximum weight increasing subseq problem, solved in $O(n\lg n)$ time
- k genomes, $O(n^k)$
- can be reduced to hitting set problem (which is equivalent to weighted set cover)
- good approximate solutions in practice using heuristics
- alignment as implicit hitting set problem
- implicit as we do not want to list all the sets, sets are the mixed cyles and there may be an exponential number of them
- however, it is easy to check whether a set H is a hitting set or not